Number Theory: Prime Numbers and Modular Arithmetic

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Factoring Polynomials: Complexity and Algorithms

Delves into the complexity of factoring polynomials and the implications for security.

Prime Number Theorem

Explores the proof of the Prime Number Theorem and its implications in number theory.

Number Theory: More Facts about Primes

Covers the distribution of primes, arithmetic progressions, Mersene primes, and Goldbach's Conjecture.

Diffie-Hellman and ElGamal Cryptosystems

Explores Diffie-Hellman key exchange, ElGamal cryptosystem, and their security applications in cryptography.

Course Overview: Teaser on Course Contents

Offers an overview of propositional and predicate logic, sets, functions, relations, algorithms, Swiss cities, sorting tables, Covid infections, poker hands, and prime numbers.

Modular Arithmetic: Understanding RSA Cryptosystem

Explores modular arithmetic and its role in the RSA cryptosystem for error detection.

Multicorrelation Sequences and Primes

Explores multicorrelation sequences, primes, and their intricate connections in number theory and ergodic theory.

Prime Gaps and Multiplicative Sieve Inequalities

Covers the Bombieri-Vinogradov theorem and its implications for prime gaps and multiplicative sieve inequalities.

Fundamental Theorem of Arithmetic

Covers prime numbers, unique decomposition of natural numbers into prime factors, and practical implications for calculations.

RSA Cryptosystem: Encryption and Decryption Process

Covers the RSA cryptosystem, encryption, decryption, group theory, Lagrange's theorem, and practical applications in secure communication.